# ---
# title: 1025. Divisor Game
# id: problem1025
# author: Tian Jun
# date: 2020-10-31
# difficulty: Easy
# categories: Math, Dynamic Programming
# link: <https://leetcode.com/problems/divisor-game/description/>
# hidden: true
# ---
# 
# Alice and Bob take turns playing a game, with Alice starting first.
# 
# Initially, there is a number `N` on the chalkboard.  On each player's turn,
# that player makes a _move_  consisting of:
# 
#   * Choosing any `x` with `0 < x < N` and `N % x == 0`.
#   * Replacing the number `N` on the chalkboard with `N - x`.
# 
# Also, if a player cannot make a move, they lose the game.
# 
# Return `True` if and only if Alice wins the game, assuming both players play
# optimally.
# 
# 
# 
# **Example 1:**
# 
#     
#     
#     Input: 2
#     Output: true
#     Explanation: Alice chooses 1, and Bob has no more moves.
#     
# 
# **Example 2:**
# 
#     
#     
#     Input: 3
#     Output: false
#     Explanation: Alice chooses 1, Bob chooses 1, and Alice has no more moves.
#     
# 
# 
# 
# **Note:**
# 
#   1. `1 <= N <= 1000`
# 
# 
## @lc code=start
using LeetCode

## add your code here:
## @lc code=end
